01-coralseed-theory.Rmdcoralseed is a spatially explicit probabilistic model
that attempts to quantify the spatial footprint of coral larval
re-seeding from restoration progjects. The model is based on
high-resolution oceanographic models (e.g. CONNIE) that allow for
tracking of individual particles following release through space and
time. By incorporating experimental data on larval behaviour
(competency, habitat specific substrate settlement preferences, swimming
behaviour) settlement probability can be modelled individually for
105 - 106 larvae. The temporal
dispersal-competency model is then overlaid onto high-resolution habitat
maps (Allen Coral Atlas)
forming a spatially-explicit probabilistic model of settlement following
release of coral larvae.
coralseed aims to provide insight into key knowledge
gaps in larval restoration: 1) Where do larvae settle following release?
2) What is the spatial footprint of larval reseeding projects? 3) what
are the likely densities of settled corals? 4) What densities of adult
corals (~10cm size) are produced from reseeding and where are they
located? By varying initial model parameters (e.g. tidal currents, time
of release, larval competency, larval densities, location of release
sites), a simulation modelling approach can be used to quantify the
likely spatial footprint and expected settlement densities, allowing for
optimisation and upscaling of larval reseeding programs on the Great
Barrier Reef and elsewhere.
coralseed model is formed from three main sections:
Probabilistic model of larval competency through time: the model is parameterised on fine-scale (hourly) data on coral settlement from wild-captured larvae cultured from the nGBR. The proportion of larvae settling through time is used to create a Bayesian probabilistic model of coral settlement in the early time period following release (0-12hrs), simulating a larval release on reef substrates.
Individual-based modelling of larval competency from dispersal models: the model leverages a high-resolution particle tracking model (CONNIE 3) that simulates particle releases from a point-source larval re-seeding project at Lizard Island (nGBR) in 2022. The model overlays the temporal trajectories from the probabilistic settlement model on spatial particle tracks to determine likely settlement times across dispersal trajectories.
Quantifying spatial mosaics of coral settlement potential
from habitat maps: By combining high-resolution
satellite-derived maps of coral habitats adjacent to release sites (https://allencoralatlas.org) with larval behaviour
determined from experimental results on settlement preferences and
habitat electivity (e.g. reef crest, reef slope), coralseed
creates spatially explicit predictions of coral settlement across
seascapes.
Below is the full code and data in R for
coralseed v0.0.0.9 with a (mostly) complete explanation of
how the model functions. coralseed is intended to be
flexible in terms of parameterisation, and can be generalised beyond the
current implementation. The document is in rmarkdown format
(Show / Hide buttons in each code section
expand code and details.
### 1. Probabilistic models of larval competency
In larval re-seeding programs, larvae are cultured (either in aquaculture facilities on land or within culture ponds at sea) and held until they reach optimal competency (usually determined by either i) adding n larvae to a tile and quantifying settlement after 10-24hrs, or ii) adding tiles to culture ponds and quantifying the proportion of larvae that settle after a 24hrs. Competency assays are repeated daily, and larvae are then released onto the reef after 3-6 days at peak of competency (i.e. highest number of settled larvae) to maximise the impact of larval reseeding.
coralseed defines competency as the duration of time
from release to settlement (from the perspective of larvae at are
n days old following fertilisation). This definition differs
from traditional studies of larval competency (e.g. Heyward
& Negri 1999, Connolly
& Baird 2010) and that derive larval competency as the
proportion of n larvae settling in a 24hr period across
multiple days. The distinction is important as coralseed
models competency as continuous (i.e. hourly measurements)
individual-based measures within a single cohort, while traditional
studies (and dispersal models) define discrete (daily) measures
across multiple cohorts.
To parameterise coralseed, we ran several experiments at
SeaSims and during coral spawning in the nGBR in 2022. The experiments
tracked settlement of replicated cohorts of larvae (n=100 per
replicate) at hourly timepoints (either 0 to 48hrs at SeaSims or 0-12hrs
with wild spawn). In all experiments, larvae were released into 1 litre
aquaria with a preconditioned settlement tile for substrate.
coralseed v0.1 uses the experimental results from
wild-captured coral larvae from Lizard Island in Dec 2022. Briefly, five
replicate pre-conditioned tiles were placed in individual 1 litre
through-flow aquaria (below left) to simulate natural conditions, and
100 larvae added to each container at t0. Tiles were imaged hourly
following larval release using a high-resolution camera (Sony a7R IV)
and in-water probe lens (Laowa 24mm) between t0-6 hrs and again at ~t10
hrs. The proportion of larvae settling through time was quantified by
tracking individual settlement through time (below right).

Quick summary of key results:
Settlement densities were similar to field experiments after 24hrs
(~1.0 settlers per cm2) at Lizard Island in Dec 2022 where
100k larvae were released into 1.5 * 1.5m net enclosures on the reef.

#### Probabilistic approach to determining
competency
One approach to modelling time-censored data is survival analysis, which explicitly considers time-to-event outcomes. Applying this to the settlement experiment, survival analysis becomes “time-to-settlement” rather than “time-to-death”. Each experimental time point can be considered as a census of 100-n larvae from the initial starting pool, with individuals undergoing a binary transition where swimming larvae = “0” and settled larvae = “1”. To estimate probability of settlement through time, the data is fit with a Bayesian discrete-time survival model with a Weibull distribution, resulting in posterior distributions for shape and scale that accounts for between-replicate variability in a multilevel framework.
The survival model is fit in brms (see code for details), where the
scale and shape parameters are resampled from the posterior draws using
scale = exp(mu) / gamma(1 + 1/k). Predictions of
time-to-competency for each individual were estimated from the Weibull
parameters (shape, scale) using the rweibull function for
each of the 10k posterior draws.
The plot below shows the model outputs: probability of settlement from initial release to t12hrs. Thick black line represents the median model output, thin lines represent 100 random draws from the posterior (highlighting variability in predicted trajectories from the multilevel approach).

Predictions for time-to-settlement for parameterising dispersal models (105 - 106 larvae) were obtained from draws from the posterior. The figure below (a) is an example of 100 posterior draws representing the probable time-to-settlement for 100 individual (ordered) particle tracks with the median probability density function of the Weibull fit. For the simulated population of n=100 larvae the model proximates the median fit, predicting 44% competence at t12hrs (56% larvae remain in an incompetent state either to settle at a later stage or undergo mortality).
The same dataset is visualised (below, figure b) as 1-dimensional trajectories of the same population of 100 larvae, where green points indicate the release of larvae at t0, and red points represent the predicted competence time for an individual larvae. Transposing these trajectories onto dispersal tracks, “competence” is used in the context of “competent and able to settle” rather than “settled” in
The trajectories are used to parameterise spatiotemporal trajectories by transposing a binary state (“not competent” vs “competent”) on particle tracks from hydrodynamic models, which rephrases the question “when do larvae become competent?” to “where are larvae in space when they become competent in time?”

The coralseed code leans heavily on
sf/lwgeom for processing data and spatially
mapping, and tmap to visualise the data (an updated v0.2
replaces tidyverse with data.table to speed
things up with large datasets).
The following example is based on a simulated larval release of 1k particles for a 0-6 hour time window (15:00 to 21:00) at Lizard Island, December 2021.
First, the model converts the imports data into sf as a
series of points for each individual particle track (id) at
12 minute time-steps from initial release:
#> options: GeoJSON
#> Reading layer `OGRGeoJSON' from data source
#> `https://www.dropbox.com/s/yj44muabx8z2laf/run_day_11656_lizard_fcst_15_2611_93.json?raw=1'
#> using driver `GeoJSON'
#> Simple feature collection with 31000 features and 3 fields
#> Geometry type: POINT
#> Dimension: XYZ
#> Bounding box: xmin: 145.4448 ymin: -14.64841 xmax: 145.4568 ymax: -14.63941
#> z_range: zmin: 1.95 zmax: 1.95
#> Geodetic CRS: WGS 84
head(particle_points_json)
#> Simple feature collection with 6 features and 3 fields
#> Geometry type: POINT
#> Dimension: XYZ
#> Bounding box: xmin: 145.454 ymin: -14.64806 xmax: 145.4543 ymax: -14.64786
#> z_range: zmin: 1.95 zmax: 1.95
#> Geodetic CRS: WGS 84
#> id decay_value time geometry
#> 1 0 1 2021-12-01 01:46:00 POINT Z (145.454 -14.64786 ...
#> 2 0 1 2021-12-01 01:57:00 POINT Z (145.4541 -14.64791...
#> 3 0 1 2021-12-01 02:09:00 POINT Z (145.4542 -14.64795...
#> 4 0 1 2021-12-01 02:21:00 POINT Z (145.4542 -14.64799...
#> 5 0 1 2021-12-01 02:33:00 POINT Z (145.4543 -14.64802...
#> 6 0 1 2021-12-01 02:45:00 POINT Z (145.4543 -14.64806...coralseed spatially interpolates each particle to 1
minute time-steps across the trajectory and randomly samples from the
output of the Bayesian time-to-settlement model to determine a
probabilistic competency point (time in minutes following release) for
each particle. points are then connected to form
paths each particle id according to their
competency state through time (either incompetent or
competent).
Below is the dispersal time since release (minutes) and larval state for 1000 individual larvae following release. For spatial reference, a “restoratation hectare” boundary (100m x 100m) is overlaid on the centre of the release site (red box).